Question

A box contains 10 white and 20 black marbles one selects at random 10 with replacement compute the probability of obtaining at least 2 white marbles

Answer 1

Probability of picking a white ball with replacement is $\frac{10}{30}=\frac{1}{3}$ . Picking balls ten time with replacement forms a Binomial distribution.

$P(\ge2)=1-P(\le1)$

$P(=0)=(\frac{2}{3})^{10}=0.0173415$

$P(=1)=\frac{10}{3}×(\frac{2}{3})^9=0.08671$

$P(≥2)=1-0.0173415-0.008671=0.895949$

Similarly the Excel formula, =1-BINOM.DIST(1,10,1/3,TRUE) can be used to obtain the probability.